1. Field of the Invention
The present invention relates to a system for and a method of controlling processes, and more particularly to a hybrid predictor and a hybrid prediction method for predicting a process output. The present invention also relates to a system for and a method of controlling processes using the hybrid predictor and hybrid prediction method.
2. Description of the Prior Art
The above-mentioned hybrid predictor is a device for generating a prediction vector by predicting a process output signal based on a process input signal in a set prediction horizon, using a model having process dynamics. The prediction vector is indicative of the predicted process output signal.
In particular, a parameter model, which can be modified in accordance with a variation in processes, is used in such a hybrid predictor. The parameter model is used to achieve a shift of prediction vectors and to obtain a step response coefficient. The hybrid predictor first predicts a process output signal based on a process input signal in a prediction horizon. Subsequently, the hybrid predictor corrects the predicted values using measured process output signals while predicting an output to be generated in a next prediction horizon, based on a process input signal value currently generated. The above procedure of the hybrid predictor is repeated to generate predicted values which are used for a process control.
It is well known that conventional feedback controllers have a limitation in controlling processes dominated by dead time and multivariable processes involving considerable interactions. In order to eliminate the limitation involved in the conventional feedback controllers, several predictive control techniques using a predictor have been developed.
FIG. 1 illustrates a conventional control loop including a process controller which performs a desired control using a conventional predictor. As shown in FIG. 1, the control loop includes a predictor 100, a reference value provider 200, a subtracter 250, a controller 300, and a process 400. The predictor 100 includes a model response unit, a prediction vector unit 140 and an horizon selection unit 150.
The process 400 receives a control signal u(k-1) from the controller 300. The process 400 also receives a measurable disturbance signal d(k-1). Based on these signals u(k-1) and d(k-1), the process 400 generates a response which is a process output signal y(k). The signals u(k-1) and d(k-1) are also applied to the model response unit 130.
The model response unit 130 is stored with step response coefficients associated with the signals u(k-1) and d(k-1). Using the stored step response coefficients, the model response unit 130 outputs a model response vector indicative of a process output signal resulting from signals u(k-1) and d(k-1) applied to the process 400 at the current step.
The prediction vector unit 140 receives the model response vector from the model response unit 130 and the process output signal y(k) from the process 400. The prediction vector unit 140 corrects the model response vector based on the process output signal y(k), thereby outputting a prediction vector Y(k/k) (Y(k/k)=[y(k), . . . y(k+n-1)]).
The horizon selection unit 150 receives the prediction vector Y(k/k) from the prediction vector unit 140 and converts it into a prediction vector having a size corresponding to a prediction horizon P which is used in the controller 300.
The subtracter 250 receives the converted prediction vector from the horizon selection unit 150 and outputs an error vector which is a difference of the prediction vector from a reference vector received from the reference value provider 200. The error vector represents the difference between a desired process output and a predicted process output.
The controller 300 receives the error vector from the subtracter 250 and outputs a controller signal u(k) based on the error vector using a control algorithm.
In the above-mentioned conventional control loop, a predictor method is utilized which uses the following truncated response model (Lee, J. H., M. Morari, and C. E. Garcia, State-space Interpretation of Model Predictive Control, Automatics, Vol. 30, No. 4, pp. 707-717, 1994). EQU Y(k+1/k)=MY(k/k)+S.sup.u .DELTA.u(k)+S.sup.d .DELTA.d(k)
where, "Y(k+1/k)" corresponds to [y(k+1), y(k+2) . . . y(k+n)].sup.T (Y(k+1/k)=[y(k+1), y(k+2) . . . y(k+n)].sup.T) and represents a prediction vector for predicting process output signals for steps from the current step k to a future step n. Also, "n" represents a model truncating order. The model truncating order is set to a value at which the process is sufficiently stable in such a manner that y(k+n)=y(k+n+1)=. . . . "S.sup.u " and "S.sup.d " are n.times.1 vectors indicative of the step response of an input signal u and a measurable disturbance signal d, respectively. In the above equation, "M" represents a vector shift matrix for shifting the vector one step. The vector shift matrix M is an n.times.n matrix. The matrix M and vectors S.sup.u and S.sup.d are expressed as follows: ##EQU1##
FIG. 2 is a view illustrating a prediction method at a time k using a conventional predictor.
In FIG. 2, the graph 200 shows the procedure of predicting a variation in the control signal u(k-1) at a time k-1 and a variation in the process output signal y(k) under the condition in which there is no variation in the control signal u(k) after a time k. The prediction vector Y(k/k), 230, of the previous step, corrected based on the process output signal y(k) measured at the time k, corresponds to "[y(k), y(k+1) . . . y(k+n-2), y(k+n-1)]" (Y(k/k)=[y(k), y(k+1) . . . y(k+n-2), y(k+n-1)]). Here, "n" is a value obtained after the process output signal y(k) sufficiently stable. The prediction vector Y(k+1/k), 240, at the time k represents a variation 220 in the process output signal y(k) occurring after a time k+1. The prediction vector Y(K+1/k) has values obtained by shifting values of the prediction vector Y(k/k) obtained after the time k+1 and already corrected at the time k as follows: ##EQU2##
In accordance with the conventional prediction method, the condition in which y(k+n-1)=y(k+n)=y(k+n+1)= . . . is established after the process is sufficiently stable, as shown by the graph 200A in FIG. 2. Accordingly, the condition in which Y(k+1/k)=[y(k+1), y(k+2) . . . y(k+n-1), y(k+n)] is established.
Since the conventional predictor should be stored with step response coefficients corresponding in number to the model truncating order n, as mentioned above, it requires a large memory capacity. Since the derived prediction vector Y(k+1/k) has a size different from the prediction horizon P used in the controller, there is a disadvantage in that the horizon selection unit 150 should be used to re-arrange the prediction vector Y(k+1/k) in such a manner that it has a size corresponding to the prediction horizon P. For a process including integrating variables, the last column of the vector shift matrix M, namely, [0 0 0 . . . -2 1], should be separately configured. Where a change in the process occurs, it is impossible to achieve an adaptive prediction for deriving again associated model response coefficients.